The United States is the one country that exists, as far as I know, and ever has, that was founded as an empire explicitly. According to the founding fathers, when the country was founded it was an “infant empire.” That’s George Washington.
The model for the founding fathers that they borrowed from Britain was the Roman Empire. They wanted to emulate it. Even before the Revolution, these notions were very much alive. Benjamin Franklin, 25 years before the Revolution, complained that the British were imposing limits on the expansion of the colonies. He admonished the British (I’m quoting him), “A prince that acquires new territories and removes the natives to give his people room will be remembered as the father of the nation.” And George Washington agreed. He wanted to be the father of the nation. His view was that “the gradual extension of our settlement will as certainly cause the savage as the wolf to retire, both being beasts of prey, though they differ in shape.”
Thomas Jefferson, the most forthcoming of the founding fathers, said, “We shall drive them [the savages] — We shall drive them with the beasts of the forests into the stony mountains,” and the country will ultimately be “free of blot or mixture” — meaning red or black. Furthermore, Jefferson went on, “Our new nation will be the nest from which America, north and south, is to be peopled,” displacing not only the red men here but the Latin-speaking population to the south and anyone else who happened to be around.
There was a deterrent to those glorious aims, mainly Britain. In particular, it blocked the invasion of Canada. The first attempted invasion of Canada was before the Revolution, and there were several others later, but it was always blocked by British force, which is why Canada exists. The United States did not actually recognize Canada’s existence until after the First World War.
Another goal that was blocked by British force was Cuba. Again, the founding fathers regarded the taking over of Cuba as essential to the survival of the infant empire.
Adams, incidentally, later in his life regretted this. He condemned the Mexican War as an executive war and a terrible precedent. And he also expressed remorse over the fate of what he called “that hapless race of Native Americans which we are exterminating with such merciless and perfidious cruelty.” They knew what they were doing.